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Author Topic: Paper Clip Top // Sakai Top  (Read 7066 times)

Iacopo

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Re: Paper Clip Top // Sakai Top
« Reply #15 on: January 04, 2017, 03:37:05 PM »

In my simple example with two masses, the centrifugal forces are still balanced during acceleration, so the center of mass will not move along the line between the masses. But there will be a force perpendicular to that line. The side with the lower moment of inertia will "get ahead" with respect to the opposite side, taking the center of mass along.

I thought the same.
Also it has come to my mind that maybe this could be part of the explanation why my unbalanced experimental top Nr. 17 at the transition height spins leaned 90 degrees after its heavy side.
So today I have arranged this top in a way to have the side with the highest moment of inertia in the opposite sector from the heavier side.
But the marks, as always, still appear 90 degrees after the heavy side.  The position of the sector with the highest moment of inertia instead seems to have no influence in the position of the brush marks.   So mistery still unsolved.
« Last Edit: January 04, 2017, 03:51:14 PM by Iacopo »
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Jeremy McCreary

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Re: Paper Clip Top // Sakai Top
« Reply #16 on: June 10, 2020, 02:38:08 PM »

Tim's recent lengthy return to the Sakai paper clip top at 2:33...

https://youtu.be/tErDu8cQtCc

BTW, there is no need to balance AMIs around an asymmetric top. All you need is dynamic (static+couple) balance about the intended spin axis. Meaning that the spin axis must pass exactly through the top's CM and align perfectly with its greatest or least principal axis.

Ultimately, this follows from 4 facts:
1. Mass is always positive.
2. Moments of inertia are always positive.
3. Moments about the same axis add (build up).
4. In the absence of air and tip resistance, two tops with identical mass properties (mass, principal axes of inertia, principal moments of inertia, and CM location) will behave exactly the same -- though still with considerable room to differ in mass, size, and shape.

A key consequence: The AMI of a point mass M orbiting an axis at radius R is identical to the AMI of a very thin circular ring of mass M and radius R centered on that axis, regardless of the ring's axial length.

In other words, AMI knows only about the squares of the distances from the spin axis to all the contributing masses -- and nothing about either their azimuths around the axis, or their locations along the axis. (On that last point, TMI is a very different story.)

So there's no way for the AMI contribution of one part of a top to offset the AMI contribution of any other. Which makes the idea of AMI balance meaningless.

Contributions to CM location combine in a totally different way -- one in which balance does make sense. Look up first and second mass moments to see why.
« Last Edit: July 02, 2020, 11:59:35 PM by Jeremy McCreary »
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Playing with the physical world through LEGO

ta0

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Re: Paper Clip Top // Sakai Top
« Reply #17 on: July 01, 2020, 12:07:27 PM »

Tim converts the Sakai paperclip top into a magnetic top. Also a paperclip tippe top and a double buzzer (that does not buzz):

https://www.youtube.com/watch?v=fZgCBMhdO18

By the way, I got the book Electric Toy Making by Sloan, 1901 edition, which has the magnetic top on the cover:



It was first published in 1891. The first chapter is all about making your own (wet) battery to make the toys work . . .  ::)
« Last Edit: July 01, 2020, 12:11:01 PM by ta0 »
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